AB INITIO CALCULATIONS OF STRUCTURAL PROPERTIES OF ZINC BLENDE QUATERNARY AlxGayIn1-x-yN ALLOYS

The wide band-gap group-III nitride semiconductors AlN, GaN, InN, and their ternary AlGaN, InAlN, InGaN alloys have been extensively investigated due to their importance for the electronic and optoelectronic device technology. Recent examples are the optoelectronic commercial devices operating in the green-blue and ultraviolet (UV) spectral regions. By allowing among the group-III nitrides one may, in principle, vary the band-gap from about 0.7-0.9 eV (InN) to 6.3 eV (AlN), range that includes the GaN band-gap of ~ 3.4 eV. A way of increasing the flexibility of nitride alloy compounds, and also to have further advantage over the ternary alloys have been achieved by using AlxGa1-xIn1-x-yN quaternary alloys. The utilization of the AlGaInN alloy has shown to be an effective approach to reduce the defect density in the device, since it permits to control independently the alloy lattice parameter and the band-gap. Hence, AlGaInN lattice-matched to GaN, or AlN may be easily produced. Based on these features, UV light-emitting diodes and laser diodes consisting of quaternary AlxGa1-xIn1-x-yN active layers have been proposed. Despite these recent developments, there are no theoretical investigations based on rigorous first principles calculations of the structural properties, such as lattice constant, etc, of quaternary AlGaInN alloys. In the present work we report on the results of first-principles calculations of structural properties of quaternary AlxGa1-xIn1-x-yN alloys. The calculations were carried out by combining a plane-wave pseudopotential approach, within the local density approximation, and the cluster expansion method together with the generalized quasi-chemical approximation to disorder and composition fluctuations in the alloy [1-3]. The cubic (zinc blende) phase of the alloy is assumed as a model system. Results are presented for the lattice constant, bulk modulus, and bond lengths in the alloy. We found that the configurationally averaged lattice constant a(x,y) versus the alloy contents x and y fulfills a Vegard’s-like law, i.e. all values of a belong to a plane surface. The range of compositions for which the quaternary alloy is lattice-matched with GaN has been obtained. A considerable bowing has been predicted for the bulk modulus as well as for the bond-lengths of the quaternary AlGaInN alloy. A comparison of the calculated lattice parameters with the available experimental data as obtained from X-ray spectroscopy measurements lead us to the conclusion that, as for the ternary nitride alloys, the currently assumed Vegard’s-like law is verified theoretically to be also valid for the quaternary AlGaInN alloys. The calculations performed here can be of great importance to guide further experiments in these alloys.